Question

find the cube root of 9261 by long division method.​

Answer 1

Answer:

first of all cube roots can never be found through the method of long division method

Step-by-step explanation:

Let us understand step by step:

Step 1: Find the prime factors of 9261

9261 = 3×3×3×7×7×7

Step 2: Pair the identical factors in a group of three and write in the form of cubes.

9261 = (3×3×3)×(7×7×7)

9261 = 3³×7³ [By exponent law: a^m xa^n = a^m+n]

9261 = (3×7)³ [By exponent law: a^m xb^m = (ab)^m]

9261 = 21³

Step 3: Apply cube root to both sides of the above expression.

∛9261 = 3√(21³)

The cube root gets cancelled by the cube of 21.

Hence, ∛9261 =21